Question
In: Statistics and Probability
a. When a fair die is thrown, numbers 1 through 6 would appear with equal probability of...
a. When a fair die is thrown, numbers 1 through 6 would appear with equal probability of 1/6. The mean is 3.5 and variance is 2.92.
If 57 dice are thrown, what is the variance of their sum?
b .
When a fair die is thrown, numbers 1 through 6 would appear with equal probability of 1/6. The mean is 3.5 and variance is 2.92.
If 40 dice are thrown, what is the mean of their sum?
c.
Let X be a Normal random variable with mean 30 and standard deviation 8. Find its 60th percentile (i.e. find a number y such that P(X < y) = 0.6)
(provide one digit to the right of decimal point)
d.
Let X be a Normal random variable with mean 30 and standard deviation 8. Find P(32 < X < 40). (provide four digits to the right of the decimal point)
Solutions
orchestra answered 1 year agoRelated Solutions
An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides...
An ordinary (fair) die is a cube with the numbers 1 through 6 on
the sides (represented by painted spots). Imagine that such a die
is rolled twice in succession and that the face values of the two
rolls are added together. This sum is recorded as the outcome of a
single trial of a random experiment. Compute the probability of
each of the following events. Event A: The sum is greater than 9.
Event B: The sum is not...
An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides...
An ordinary (fair) die is a cube with the numbers 1 through 6 on
the sides (represented by painted spots). Imagine that such a die
is rolled twice in succession and that the face values of the two
rolls are added together. This sum is recorded as the outcome of a
single trial of a random experiment.
Compute the probability of each of the following events.
Event A: The sum is greater than 9
Event B: The sum is not...
A die is thrown twice and the sum of the numbers rising is noted to be 6.
A die is thrown twice and the sum of the numbers rising is noted to be 6. Calculate the is the conditional probability that the number 4 has arrived at least once?
An ordinary (fair) die is a cube with the numbers through on the sides (represented by...
An ordinary (fair) die is a cube with the numbers through on the
sides (represented by painted spots). Imagine that such a die is
rolled twice in succession and that the face values of the two
rolls are added together. This sum is recorded as the outcome of a
single trial of a random experiment. Compute the probability of
each of the following events.
Event A : The sum is greater than 5 .
Event B: The sum is an...
Suppose you roll a fair 15 sided die. The numbers 1-15 appear once on different sides....
Suppose you roll a fair 15 sided die. The numbers 1-15 appear
once on different sides. (Imagine a regular die with 12 sides
instead of 6.) Answers may be left in formula form.
(a) What is the probability of rolling a 7?
(b) What is the probability of rolling an odd number and a
number greater than 8?
(c) What is the probability of rolling an even number or a
number greater than 9?
(d) Suppose you roll the die,...
A fair red die and a fair green die are rolled. (a) What is the probability...
A fair red die and a fair green die are rolled.
(a) What is the probability that the sum of the numbers is
even?
(b) What is the probability that the number on the red die is
more than the number on the green die?
(c) What is the probability that the number on the red die is
twice the number on the green die?
(d) What is the probability that the number on the red die is
different from...
Let X equal the outcome (1, 2 , 3 or 4) when a fair four-sided die...
Let X equal the outcome (1, 2 , 3 or 4) when a fair four-sided
die is rolled; let Y equal the outcome (1, 2, 3, 4, 5 or 6) when a
fair six-sided die is rolled. Let W=X+Y.
a. What is the pdf of W?
b What is E(W)?
Create a die, which will roll a 6 with probability of 50% and all other numbers...
Create a die, which will roll a 6 with probability of 50% and
all other numbers (1-5) with equal probability. What is E(Y) if Y
was the outcome of that die? and X is the result of the fair
die.
sd(Y)
var(X-2Y)
Please write the code in R
Suppose we roll a fair 6 sided die with the numbers [1,6] written on them. After...
Suppose we roll a fair 6 sided die with the numbers [1,6]
written on them. After the first die roll we roll the die ? times
where ? is the number on the first die roll. The number of points
you score is the sum of the face-values on all die rolls (including
the first). What is the expected number of points you will
score?
Consider that you toss a fair 6-sided die containing the numbers 1-2-3-4-5-6 and also toss a...
Consider that you toss a fair 6-sided die containing the numbers
1-2-3-4-5-6 and also toss a fair 4-sided die containing the numbers
1-2-3-4. Find the probability distribution for the sum of the
values on the two dice. Also, find the mean and the variance of
this probability distribution.
Please provide a well written and well explained answer.
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